Spatial harmonic traveling wave tube



Nov. 5, 1957 S. D. ROBERTSON SPATIAL HARMONIC TRAVELING WAVE TUBE FiledDec. 30, 1952 INVENTOR S. D. ROBERTSON By J. MIA? 7 A TTORA/EVpropagating.

United States Patent-O SPATIAL HARMONIC TRAVELING WAVE TUBE Sloan D.Robertson, Fair Haven, N. J., assignor to Bell Telephone Laboratories,Incorporated, New York, N. Y., a corporation of ew York ApplicationDecember 30, 1952, Serial No. 328,579

7 Claims. (Cl. 315-3.5)

This invention relates to microwave devices and more particularly tosuch devices of the so-called traveling wave type.

The principal object of this invention is to simplify the structure of awave guiding circuit useful for amplification or generation ofelectromagnetic waves at millimeter wavelengths.

Another object is to achieve broad band amplification intraveling wavetubes without sacrificing gain and ease of construction.

Microwave devices of the so-called traveling wave type which cause thetransfer of energy from an electron stream to an electromagnetic wavepropagating along the circuit offer one particular advantage not foundin other amplifying devices, namely, useful amplification over a verybroad band of frequency. Since this band width, expressed as apercentage of the operating frequency, is relatively fixed, it isdesirable to raise the frequency of operation as much as possible to avalue where, for example, a band width of ten percent covers manythousands of megacycles. Unfortunately, however, as the frequency ofoperation is increased various difiiculties are encountered. Forexample, a helix such as is commonly used in traveling wave tubes forpropagating a fast electromagnetic wave has been employed in a tubeoperating at roughly 50,000 megacycles but the amplification of the tubeis so limited and the helix is so difiicult to manufacture because ofits microscopic size that such a structure is not very satisfactory. Analternative approach to these problems has been suggested by S. Millmanin an article A spatial harmonic traveling wave amplifier for sixmillimeters wavelengt appearing in the Proceedings of the Institute ofRadio Engineers, volume 39, page 1040, September 1951.

The present invention makes use of the spatial harmonic principle or"operation and for a comprehensive exposition thereof the reader isreferred to the above-mentioned article. Briefly though, it may be saidthat this principle consists essentially in causing an electron streaminteracting with an electromagnetic wave to interact only at givenintervals. This is accomplished by beaming the electron stream inelectrical proximity to a series of regularly spaced discontinuitiesalong which a wave is These discontinuities are chosen so that thereexists between them a component of electric field parallel to thedirection of electron flow and so that no such component exists in theregion over them. By adjusting the velocity of the electron stream, agiven electron can be made to reach each interval betweendiscontinuities at a time when the electric field intensity here is thesame as it was in the preceding interval when this electron arrivedthere. The electrons can thus be synchronized in phase with any wavewhich propagates along these discontinuities with a component of phasevelocity parallel to the electron flow equal to the velocity of theelectrons plus' a velocity such that the electric field rotates anymultiple of 2360 degrees between successive A interaction intervals.

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In accordance with the present invention, an electron stream is beamedin coupling relation to the electric field existing in the vicinity of aseries of regularly spaced discontinuities of basically simpleconstruction positioned within a conductively bounded wave guiding path.These discontinuities, which can be made more uniformly and much moreeasily than structures used for a similar purpose heretofore, are, inone specific embodiment, formed by a plurality of slot-like openingsperforating a thin sheet while in a second embodimentthey are formed byparallel spaced turns of wire having slot-openings between them. A morecomplete understanding, however, of the nature and the objects'of thisinvention may be gained fromthe following description thereof given inconnection with the accompanying drawings of several illustrativeembodiments. With reference to the drawings in general:

Fig. 1 is a perspective view of an embodiment of a spatial harmonic Waveguiding circuit in accordance with the invention comprising arectangular waveguide surrounding a raised hollow rectangular ridge inthe surface of' whichthere are a plurality of regularly spaced slot-likeopenings;

Fig. 2 shows in perspective view a section of a second embodiment'of aspatial harmonic wave guiding circuit similar to that of Fig. 1 but inwhich the discontinuities are formed by parallel turns of a wire wrappedupon a U-shaped channel; and

Fig. 3 is a side section of a backward traveling wave oscillator inwhich a circuit similar to that shown in Fig. 2 is a component part.

Referring now more particularly to the drawings, there is shown in Fig.1, by way of example for purposes of illustration, a wave guidingcircuit 10 adapted to propagate an electromagnetic wave therethroughpast a series of slot-resonators formed by slot-like openings in aconducting surface so that the wave may interact with an electron streambeamed in coupling relation to these resonators. Wave energy, which mayhave a phase velocity along the circuit greater than the speed of light,may then extract energy from the electronstream traveling in the samedirection as the wave with a velocity, for example, of one-twentieth thespeed of light.

Wave circuit 10 comprises a rectangular wave guide 11 surrounding ahollow rectangular ridge 12 which is centered along the bottom wall ofthe guide and which may be brazed or soldered to it. In the uppersurface 13 of this ridge, which is parallel to 'the'upper and lowersurfaces of the guide surrounding it, there are a plurality of,slot-like, openings 14 which are. regularly spaced a distance d apartalong the direction of wave propagation. These openings, together withthe metal between them, form slot-resonators lying transverse to thedirection of wave propagation. They are of width w and have a length lwhich makes them one-quarter wavelength resonant at the upper cut-offfrequency of the circuit. The lower cut-off frequency of guide 11 islowered somewhat along its center length by ridge 12 and an increase inthe operating band width is thereby obtained. The amount that this lowercut-01f frequency is altered depends upon the relative dimensions of theridge and its surrounding Wave guide, but a ridge of outsidemeasurements roughly equal to five-eighths the inside measurements ofits associated guide is satisfactory. The wall thickness of ridge 12 isnot critical but it should be thin compared to the free space wavelengthof i'o'perati'on. Longitudinal -slit 15, which is cut in wall 13perpendicular to openings 14., provides a convenient passage forelectron stream 16, past the series of slot-resonators. This slit hasnegligible electrical effect upon the action of the slot-resonators andit may be eliminated if not wanted by placing, for example, the twosections of wall 13 together. Its use, however, is desirable since itserves additionally to prevent the 3 metal between openings 14 frombuckling out of the plane of wall 13 when this wall is unevenly heated.

Electron gun 17 and collector electrode 18 are aligned with respect tocircuit so that the electron stream flows along the axis of slit throughthe openings in the lower wall of guide 11 provided for this purpose.Non-magnetic envelopes 19, surrounding these electrodes, together withwindows (not shown) in ends 20 and 2.1 of guide 11 and the metal wallsthereof, form an air-tight enclosure.

The curved ends of guide 11 provide a simple and effective means ofimpedance matching between the length of circuit 10 which includes ridge12 and the input and output wave guides which may be attached at ends 20and 21 respectively. Ridge 12 may be inserted through openings in thelower Wall of the guide and soldered or brazed in place so that thecurvature of this wall will provide an effective tapering of the ridgeheight. The inside dimensions of wave guide 11 are preferably chosen sothat it will propagate a transverse electric Wave in the fundamentalmode with the electric field'perpendicular to the upper and lower wallsof the guide. The conducting elements of circuit 10 are preferably madeof the same metal such as copper or silver plated molybdenum.

A parallel extending magnetic field is provided for focusing theelectron stream. A single line of magnetic flux (,0, parallel toelectron stream 16, is shown in Fig. 1 to indicate the orientation ofthis field relative to circuit 10. The elements for generating thisfield have not been shown in order to simplify the drawing but anyappro- 3 priate means may be used such as magnet poles and 51 shown inFig. 3.

In operation, a transverse electric wave is preferably applied tocircuit 10 by some appropriate means, such as a wave guide of the samedimensions as guide 11. this wave propagates from the gun end 20, of thecircuit to the collector end, it is amplified by spatial harmonicinteraction with the electron stream. This spatial harmonic phenomenonmay best be understood by a consideration of the following abbreviatedmathematical analysis adapted specifically to the structure shown inFig. 1 but applicable to spatial harmonic action in general.

If 2 is the direction of wave velocity in the wave guide, then in thevicinity of recurrent discontinuities in the guide the z component of atraveling wave may be written Ez -F(z)e (1) in which 0) is the radianfrequency and 71=m 1 (2 A exp j(21rn+0)%:|

(grad-M51) 5) tube.

From this last equation it can be seen that near the slotdiscontinuities in the wave guide there appears to be an infinite numberof spatial harmonic components of the fundamental wave, each travelingat a different phase velocity given by in which n is an integer betweenw and Setting ":0 we see that the fundamental wave travels in thepositive z direction with a phase velocity of For n=l, a wave appears totravel in the positive 1 direc tion with a velocity of which is lessthan the velocity for the fundamental wave. Similarly for other positivevalues of n. For n=-1, there appears to be a wave traveling in thepositive z direction with a phase velocity which is negative sincefundamental phase displacement 0 between successive slots is less than21r. Thus for each negative integer 21 there corresponds a wave havingnegative phase velocity, or, in other words, a backward traveling wave.The group velocity of all spatial harmonic waves, it should beremembered, is always in the direction of power propagation and is thesame for all, including those which have negative phase velocity.

In the vicinity of the guide wall between slots, that is the metalregion between slots 14, the electrons see substantially no z componentof electric field, while when passing over a slot opening they see astrong z direction electric field. This alternate passage from driftspace to interaction space is analogous to a stroboscopic light flashingon a patterned wheel, the duration of each flash corresponding to thetime the electrons are in the rc action space over the slot opening, theinterval between flashes corresponding to the time it takes an electronto go from one slot center to the next and the angular velocity of theWheel corresponding to the phase velocity of the fundamental spatialharmonic of the traveling wave. For a given wheel velocity there will bea stroboscopic frequency at which the wheel appears stationary and thisapparent non-rotation of the wheel corresponds to synchronism between aspatial harmonic of the wave and the electrons. In this synchronouscondition a single electron sees the same field vector as it passes eachslot opening and therefore the requirement for electromagnetic-waveelectron-stream interaction is met by, in effect, fooling theelectrons."

By assuming that the group velocity of the wave propagating down theguide is opposite to the velocity of electron flow, it can be seen,following the above analogy. that the electrons can be synchronized witha spatial harmonic of the wave having a negative phase velocity relativeto the group velocity. When such conditions actually exist in a spatialharmonic tube, electromagnetic power flows from the collector end to thegun end of the This mode of operation, useful for amplification up to acritical value of beam current, is likewise useful for obtainingoscillations beyond this critical value since the necessary feedbackpath for sustaining the oscillations is then automatically provided bythe electron stream.

From an inspection of Fig. 1, it is apparent that somewhere between thecondition where the slot spacing (1 equals slot width w, in which casethere is substantially no interaction between the electromagnetic waveand the electron stream, and the condition where width w of the slotopening is zero, in which case the interaction is likewise zero, theremust be some ratio of slot width to'slot spacing which gives optimuminteraction if there is to be any net gain. Now, it can be shown thatthe electron velocity Ve required for synchronization is given by andsetting the result equal to zero, the gain is seen to be maximum when 22.33 d (21rn+0) As mentioned previously, practical values of may beroughly between and so, from Equations 6 and 8, w is easily determinedfor a given electron velocity Ve, a given value of n and a givenfrequency of operation.

The slot spacing anddimensions in the circuit shown in Fig. 1 may bechosen according to Equations 6 and 8 for synchronization of theelectron stream with either forward or backward traveling spatialharmonic waves. The number of slots used will depend upon the gaindesired but approximately 100 are sufiicient for ordinary gainrequirements. It should be understood that a structure designed for aparticular mode of spatial harmonic operation at a given frequency andwith an electron stream having a certain velocity may be usedadditionally to obtain interaction between waves having the same orslightly diiferent frequencies and electron streams having greatlydifferent velocities. The following dimensions, which are given merelyfor the purpose of illustration, have been found satisfactory in acircuit built according to the design shown in Fig. l forsynchronization between the first forward spatial harmonic wave and anelectron stream having a velocity equivalent to approximately 1300volts: length 1:0.220), distanced=0.086 width w=.0.025)\ and width ofslit 15=0.065 where A is the free space wavelength at the centerfrequency of operation. I

Fig. 2 shows in perspective a portion of the center section of a spatialharmonic circuit 30 similar to that shown in Fig. 1. Here theslot-resonators are formed by parallel turns of wire 31 which liesubstantially transversely across the top of supporting U-shaped channel32. The pitch with which this wire is wrapped around the channeldetermines the slot spacing d while this'pitch, together with the wirediameter, determines the width of the opening between turns. The lengthacross the top of the channel of the turns of wire 31 in the absence ofa longitudinal slit equivalent to slit 15 in Fig. 1 is such that theseturns, together with the openings between them,

are half-wave resonant at the upper cut-off frequency of the circuit.Wave guide 33, which surrounds the wire wound channel or ridge, may beidentical to guide 11 in Fig. 1, although it is not necessarily so. Asin Fig. 1 this ridge is fastened along the bottom wall of the guide andis centered between the side walls thereof. An electron gun andcollector electrode (not shown), similar to those shown in Fig. 1, maybe used with circuit 30 to beam an electron stream just over and justunder the turns of wire 31. Means (not shown) for producing a magneticfield aligned with the axis of the electron stream may be similar tothose shown in Fig. 3. I

It is not necessary that wire 31 be of any particular cross section, butit is preferably round, as shown, or ribbon-shaped, having a thicknessless than its width. The thickness of this wire is not critical but aswith the thickness of ridge walls in circuit 10, it should be muchsmaller than a free space wavelength at the frequency of operation. Formechanical stability the wire should preferably be wrapped tightlyaround channel 32, although, alternative to this, lengths of wire may belaid across the channel opening and firmly fastened in position by aframe or by other appropriate means.

Any one of these wire structures is particularly adapted to backwardspatial harmonic wave operation since the ratio of space between thewires w to wire spacing d can readily be made to satisfy Equations 6 and8 for negative integers. A ratio of has been found suitable in thesestructures for synchronization of the electron stream with the firstbackward wave. A smaller ratio in the vicinity of one-third should beused with the first forward Wave.

The operation of wave guiding circuit 30 is substantially the same asthat of circuit 10 in Fig. 1 and it is only necessary to mention herethat for backward spatial harmonic amplification, wave energy should befed into the collector end of the circuit and extracted from the gun endthereof.

It should be understood that none of the wave guiding circuits describedin the foregoing is limited to spatial harmonic wave amplification sinceany one of these structures, if it has the requisite dimensions, may beused for the generation of wave energy by either conventional or bybackward wave operation. Conventional oscillations may be obtained inany amplifier simply by returning a sufficient portion of the outputenergy to the input of the amplifier and the operation of such anarrangement is so well known that more of a description here would besuperfluous. The generation of backward wave oscillations, on the otherhand, is a recent development in the art and, in view of the importanceof the present invention in this regard, a brief description of abackward wave oscillator is appropriate.

Fig. 3 is a side view illustration of a backward wave oscillator inwhich a circuit 40, substantially the same as circuit 30, is the wavepropagating element. This circuit is aligned with respect to electrongun 41 and collector cavity 42 so that electron stream 43 flows justover-and just under the "turns of wire 44 wrapped around channel 45. Atthe collector end of the circuit, lossy material 46 is positioned withinguide 47 on either side of channel 45 in order to minimize reflection ofwave energy at this point. Any wave energy which may be returned fromthe output connection at the gun end by impendance mismatches is therebysubstantially reduced and its unwanted interference with energypropagating in the opposite direction is mostly eliminated. At the gunend of the circuit oscillating wave energy is extracted from the circuitby a continuation of guide 47 which is bent downward for impedancematching as explained previously. An appropriate opening is provided inthe curved section of the top wall of the guide for the passage ofelectron stream 43. Guide 47 is sealed through envelope 48 and thisennet poles 50 and 51,, forms an air-tight enclosure surrounding theelectron stream. Opening 42 in pole piece 51 is shaped approximately asshown in order to reduce secondary emission from this pole which servesadditionally as a collector electrode. All the elements in the regionbetween pole pieces should be non-magnetic so that the magnetic fieldmay be made to focus the electron stream along an axis with which thefield is aligned.

When the current density of the electron stream in the arrangement shownin Fig. 3 exceeds a certain critical value, oscillations may suddenlybegin at a frequency which is determined by the stream velocity. Waveenergy, originating at the collector end of circuit 40, flows toward theoutput end thereof where it is led off through window 49 to anappropriate output connection. As this energy passes along the wirewound ridge within guide 47 it is amplified by interaction between thebackward traveling spatial harmonic of itself which is synchronized withthe electron stream and the electron. stream. This interaction, at thesame time, causes a bunching of the electron stream. This bunching inturn causes an increase in wave energy which in turn causes a bunchingof the electron stream and so on. Thus the feedback energy necessary tosustain oscillations is automatically returned to the circuit by theelectron stream. Since the frequency of oscillation is determinedprincipally by the electron velocity for a given wave guiding structureand since this velocity is easily varied electrically over a wide range,the frequency may be modulated at a high rate and with a very broad bandwidth.

The invention described herein is not limited solely to the embodimentsshown since it may include spatial harmonic wave guiding structures ofother than rectangular cross section. Furthermore, the input and outputconnections described above in connection with the drawing may bereplaced by equivalent means without altering the nature of thisinvention. Lastly, it will be apparent to those skilled in the art thatthe dimensions of the Wave guiding circuits shown in the accompanyingdrawing may be selected over a wide range without departing from thespirit or scope of the invention as set forth.

What is claimed is:

l. in a microwave device, means for forming and projecting an electronstream for interaction with an electromagnetic wave propagating parallelto the axis of said stream and with higher phase velocity than thevelocity of the stream, conductively bounded rectangular wave guidingmeans adapted to propagate an electric wave therethrough, and iterativefilter means positioned asymmetrically within said guiding meansparallel to the direction of wave propagation, said filter meansincluding a conductively bounded hollow rectangular member the lateraldimension of which is less than the lateral dimension of said waveguiding means, one wall of said member being perpendicular to theorientation of the wave electric field and in which there are aplurality of substantially transverse slot-like openings regularlyspaced in the direction of wave propagation.

2. In a microwave device, means for beaming an elec tron stream along apath. and conductively bounded wave guiding means adapted to propagatetherethrough in a direction parallel to said path an electromagneticwave for interaction with said electron stream, said wave guiding meansincluding a wave guide surrounding a raised hollow ridge one surface ofwhich is formed by a plurality of transverse slot-resonators regularlyspaced in the direction of wave propagation said ridge having a lateraldimension less than the lateral dimension of said wave guiding means.

3. In a microwave device, means for beaming an elec- (ill tron stream.along a path, and conductively bounded wave guiding means adapted topropagate therethrough in a direction parallel to said path anelectromagnetic wave for interaction with said electron stream, saidwave guiding means including a rectangular wave guide surrounding ahollow rectangular ridge one surface of which is formed by a thinconducting sheet perforated by a plurality of transverse slot-likeopenings regularly spaced in the direction of wave propagation, thesurfaces of said ridge adjacent said thin sheet being spaced from thewalls of said wave guiding means.

4. In a microwave device, means for beaming an electron stream along apath, and conductively bounded wave guiding means adapted to propagatetherealong in a direction parallel to said path an electromagnetic wavefor interaction with said electron stream, said wave guiding meansincluding a rectangular wave guide surrounding a hollow rectangularridge one surface of which is formed by parallel spaced turns of wirelying substantially parallel to the direction of wave propagation, thesurfaces of said ridge adjacent said one surface being spaced from thewalls of said guiding means.

5. In a traveling wave tube, means for beaming an electron stream alongan axis, and conductively bounded wave guiding means adapted topropagate therethrough an electromagnetic wave for interaction with saidelectron stream, said wave guiding means including a length of waveguide whose ends are bent out of line from the electron path and whosecenter section surrounds a raised hollow ridge having in one surfacethereof a plurality of slot-resonators lying transverse to the directionof wave propagation and regularly spaced apart in this direction, thelateral dimension of said ridge being less than the lateral dimension ofsaid wave guide.

6. A traveling wave tube comprising means for beaming an electron streamalong a fixed path, an air-tight envelope surrounding said means, andwave propagating means adapted to cause interaction between said clec'tron stream and an elecromagnetic wave propagating through said wavepropagating means in a direction parallel to said fixed path, said wavepropagating means including a rectangular wave guide asymmetricallysurrounding a hollow rectangular ridge whose surface perpendicular tothe electric field is formed by a plurality of slot-resonators lyingsubstantially transverse to the direction of wave propagation andregularly spaced apart in this direction, the surfaces of said ridgeadjacent said slotted surface being spaced from the walls of said waveguiding means.

7. In a microwave device, means for propagating therethrough anelectromagnetic wave at a speed less than the speed of light said meansincluding a raised hollow ridge having in a surface thereof a pluralityof slot openings lying substantially transverse to the direction of wavepropagation and spaced apart in that direction, and a rectangular waveguide asymmetrically surrounding said ridge, the lateral dimension ofsaid ridge being less than the lateral dimension of said wave guide.

References Cited in the file of this patent UNITED STATES PATENTS2,395,560 Llewellyn Feb. 26, 1946 2,567,748 White Sept. ll, 19512,604,594 White July 22, 1952 2,623,121 Loveridge Dec. 23, 1.9522,647,175 Sheer July 28, 1953 2,708,236 Pierce May 10, 1955 OTHERREFERENCES Article entitled Millimeter Waves, by I. R. Pierce, pp. 2429,Physics Today, for November 1950.

